IRR is 7.71%
Kerry Back
IRR is 7.71%
\[\text{NPV} = c_0 + \frac{c_1}{1+r} + \frac{c_2}{(1+r)^2}+ \cdots + \frac{c_n}{(1+r)^n}\]
So, NPV = 0 is a polynomial equation, which in general can have many or zero real roots.
For usual projects (negative early and positive late):
Or, in Excel, =IRR(range) computes the IRR. First element of the range is date-0 cash flow, next element is date-1 cash flow, etc.